Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium

[+] Author and Article Information
Kamel Hooman

School of Engineering, The University of Queensland, Brisbane, Australia

Ali A. Merrikh

 Applied Thermal Technologies LLC, 2700 Via Fortuna, Suite 301, Austin, TX 78746

J. Heat Transfer 128(6), 596-600 (Dec 16, 2005) (5 pages) doi:10.1115/1.2188510 History: Received August 24, 2005; Revised December 16, 2005

A theoretical analysis is presented to investigate thermally and hydrodynamically fully developed forced convection in a duct of rectangular cross section filled with a hyper-porous medium. The Darcy-Brinkman model was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e., the H boundary condition in the terminology of Kays and Crawford (1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, NY), is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic of the studied problem

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Figure 2

Midplane normalized velocity predicted by Eq. 7 and midplane dimensionless temperature profile predicted by Eq. 16, versus z∕a for some values of s and a

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Figure 3

(a) Plots of the friction factor by Eq. 10 versus s for various aspect ratios and (b) plots of the Nusselt number predicted by Eq. 20 versus s for various aspect ratios



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